In addition to .GIF, LICEcap supports its own native lossless .LCF file format, which allows for higher compression ratios than .GIF, higher quality (more than 256 colors per frame), and more accurate timestamping. If you record to .LCF, you can play back the .LCF files within REAPER (and/or use it to convert to .gif or another video format).

LICEcap is GPL free software, each download package includes the source.